Sounds like a sweet gig! and... nice mike selection
Just a comment about how you mentioned you'd mix it: Have you considered mixing the band as it would sound in a normal concert setting? All instruments filling the stereo image left to right, as they would sit on stage, maybe drums, bass, and piano off center? I've never mixed a big band like you're mentioning, but I do know that Ive loved the mixes I've done and heard that are more standard images. Just food for thought...
Let us know how it all goes!